Conceptual Mathematics introduces the concept of category to beginning students and practising mathematical scientists based on a leisurely introduction to the important categories of directed graphs and discrete dynamical systems. The expanded second edition approaches more advanced topics via historical sketches and a concise introduction to adjoint functors.
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F. William Lawvere is a Professor Emeritus of Mathematics at the State University of New York. He has previously held positions at Reed College, the University of Chicago and the City University of New York, as well as visiting Professorships at other institutions worldwide. At the 1970 International Congress of Mathematicians in Nice, Prof. Lawvere delivered an invited lecture in which he introduced an algebraic version of topos theory which united several previously 'unrelated' areas in geometry and in set theory; over a dozen books, several dozen international meetings, and hundreds of research papers have since appeared, continuing to develop the consequences of that unification.
Stephen H. Schanuel is a Professor of Mathematics at the State University of New York at Buffalo. He has previously held positions at Johns Hopkins University, Institute for Advanced Study and Cornell University, as well as lecturing at institutions in Denmark, Switzerland, Germany, Italy, Colombia, Canada, Ireland, and Australia. Best known for Schanuel's Lemma in homological algebra (and related work with Bass on the beginning of algebraic K–theory), and for Schanuel's Conjecture on algebraic independence and the exponential function, his research thus wanders from algebra to number theory to analysis to geometry and topology.
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